Fractal Approximation of Image Blocks and  Block Fractal Approximation Code

doi:10.11834/jig.1997011252

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Fractal Approximation of Image Blocks and Block Fractal Approximation Code
Vol. 2, Issue 11, Pages: 801(1997)
Published：1997
DOI： 10.11834/jig.1997011252
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DOI：

Fractal Approximation of Image Blocks and Block Fractal Approximation Code[J]. Journal of Image and Graphics, 1997, 2(11): 801. DOI： 10.11834/jig.1997011252.

摘要

提出了一种图象块的分形近似方法。该方法借助于SAS以达到对图象块的最小平方的分形近似，其运算量仅为2×M×N次乘法和4×M×N次加法，M×N为图象块大小。由图象块分形近似量化而成的编码，称之为分块分形近似编码。其压缩比依赖于所选取图象块大小和迭代变换系数的量化。对8×8图象块，在不失真情况下，其压缩比达到17.8倍。通过对大量图象的实验结果表明，只需进行8次迭代，就能得到满意的重构图象。和其它分形编码相比，此方法简洁，编码速度快，对220×220的＂Lena＂图象进行编码，在PC486/DX33上，仅需时

Abstract

A method for approximation of image block is presented

based on a least squares fractal approximation by a Self Affine System。The computational cost is only equal to 2×M×N products and 4×M×N additions。The code of image block consists of the quantized fractal cofficients。This block coding of images is called as block fractal approximation code (BFAC)。Its compression ratio depends on the size of image block and quantization of fractal cofficients。BFAC for "Lena" image by 8×8 blocks is quantized to six bits and encodes to a comp ression ratio of 17.8:1

its encoding and decoding time is about 30 seconds in PC486?D X33。A f ter eight iterations of decoding

the reconstructive image look like the origin。Its greater speed and simplicity compared to other fractal transforms suggest its immediate applicability。